If three marbles are picked at random, what is the probability

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A basket contains 4 red, 5 blue and 3 green marbles

If three marbles are picked at random, what is the probability that either all are green or all are red ?

1. 7/44
2. 7/12
3. 5/12
4. 1/44
5. None of the above

Correct Option: D

Total number of ways of selection of 3 marbles out of 12
= n(S) = ¹²C₃ = 220
Total number of favorable events = n(E)
= ³C₃ + ⁴C₃ = 1 + 4 = 5
∴ Required probability
= 5/220 = 1/44